Computerized matrix factorization and completion to infer median/mean confidential values

ABSTRACT

In an example embodiment, an anonymized set of confidential data values is obtained for a plurality of combinations of cohorts having a first attribute type and a second attribute type. A matrix of the confidential data values having the first attribute type as a first axis and the second attribute type as the second axis is constructed. A set of candidate low rank approximations of the matrix is calculated using an objective function evaluated using a set of candidate data transformation functions, the objective function having one or more parameters and an error function. One or more parameters that minimize the error function of the objective function are minimized to select one of the candidate low rank approximations of the matrix. Then one or more cells that are missing data, of the selected one of the candidate low rank approximations of the matrix, are inferred.

TECHNICAL FIELD

The present disclosure generally relates to computer technology forsolving technical challenges in collection and maintenance ofconfidential data in a computer system. More specifically, the presentdisclosure relates to using computerized matrix factorization andcompletion to infer median/mean confidential values.

BACKGROUND

In various types of computer systems, there may be a need to collect,maintain, and utilize confidential data. In some instances, users may bereluctant to share this confidential information due to privacyconcerns. These concerns extend not only to pure security concerns, suchas concerns over whether third parties such as hackers may gain accessto the confidential data, but also to how the computer system itself mayutilize the confidential data. With certain types of data, usersproviding the data may be somewhat comfortable with uses of the datathat maintain anonymity, such as the confidential data merely being usedto provide broad statistical analysis to other users.

One example of such confidential data is salary/compensationinformation. It may be desirable for a service such as a socialnetworking service to request its members to provide information abouttheir salary or other work-related compensation in order to providemembers with insights as to various metrics regardingsalary/compensation, such as an average salary for a particular job typein a particular city. There are technical challenges encountered,however, in ensuring that such confidential information remainsconfidential and is only used for specific purposes, and it can bedifficult to convince members to provide such confidential informationdue to their concerns that these technical challenges may not be met.

Additionally, certain types of combinations of cohorts may have sparseconfidential data submitted. For example, in the case of salaryinformation, certain combinations of locations and job titles may nothave enough actual submitted confidential data points in order toprovide meaningful statistical insights.

BRIEF DESCRIPTION OF THE DRAWINGS

Some embodiments of the technology are illustrated, by way of exampleand not limitation, in the figures of the accompanying drawings.

FIG. 1 is a block diagram illustrating a confidential data collection,tracking, and usage system, in accordance with an example embodiment.

FIGS. 2A-2C are screen captures illustrating an example of a userinterface provided by a confidential data frontend, in accordance withan example embodiment.

FIG. 3 is a flow diagram illustrating a method for confidential datacollection and storage, in accordance with an example embodiment.

FIG. 4 is a diagram illustrating an example of a submission table, inaccordance with an example embodiment.

FIG. 5 is a flow diagram illustrating a method for confidential datacollection and storage, in accordance with an example embodiment.

FIG. 6 is a diagram illustrating an example of a first submission tableand a second submission table, in accordance with an example embodiment.

FIG. 7 is a flow diagram illustrating a method of inferring median/meanconfidential data values in accordance with an example embodiment.

FIG. 8 is a flow diagram illustrating a method of constructing low rankapproximations of the matrix, in accordance with an example embodiment.

FIG. 9 is a flow diagram illustrating a method for optimizing parametersto obtain the best low rank approximation matrix, in accordance with anexample embodiment.

FIG. 10 is a flow diagram illustrating a method of inferringconfidential data values for entries not present in the original matrix,in accordance with an example embodiment.

FIG. 11 is a block diagram illustrating a representative softwarearchitecture, which may be used in conjunction with various hardwarearchitectures herein described.

FIG. 12 is a block diagram illustrating components of a machine,according to some example embodiments, able to read instructions from amachine-readable medium (e.g., a machine-readable storage medium) andperform any one or more of the methodologies discussed herein.

DETAILED DESCRIPTION

The present disclosure describes, among other things, methods, systems,and computer program products. In the following description, forpurposes of explanation, numerous specific details are set forth inorder to provide a thorough understanding of the various aspects ofdifferent embodiments of the present disclosure. It will be evident,however, to one skilled in the art, that the present disclosure may bepracticed without all of the specific details.

In an example embodiment, an architecture is provided that gathersconfidential information from users, tracks the submission of theconfidential information, and maintains and utilizes the confidentialinformation in a secure manner while ensuring that the confidentialinformation is accurate and reliable.

FIG. 1 is a block diagram illustrating a confidential data collection,tracking, and usage system 100, in accordance with an exampleembodiment. A client device 102 may utilize a confidential data frontend104 to submit confidential information to a confidential data backend106. In some example embodiments, the confidential data backend 106 islocated on a server-side or cloud platform 107 while the confidentialdata frontend 104 is directly connected to or embedded in the clientdevice 102. However, in some example embodiments, the confidential datafrontend 104 is also located on the server-side or cloud platform 107.

There may be various different potential implementations of theconfidential data frontend 104, depending upon the type andconfiguration of the client device 102. In an example embodiment, theconfidential data frontend 104 may be a web page that is served to a webbrowser operating on the client device 102. The web page may includevarious scripts, such as JavaScript code, in addition to HypertextMarkup Language (HTML) and Cascading Style Sheets (CSS) code designed toperform various tasks that will be described in more detail below. Theweb page may be served in response to the user selecting a link in aprevious communication or web page. For example, the link may bedisplayed in an email communication to the user or as part of a feedsection of the user's social networking service member page. This allowsthe entity operating the confidential data collection, tracking, andusage system 100 to selectively target users to request that they submitconfidential information. For example, the entity may determine thatthere is a need to obtain more salary information for users from Kansasand then may send out communications to, or cause the social networkingservice to alter feeds of, users in a manner that allows the users toselect the link to launch the confidential data frontend 104.

In another example embodiment, the confidential data frontend 104 may bebuilt into an application installed on the client device 102, such as astandalone application running on a smartphone. Again this confidentialdata frontend 104 is designed to perform various tasks that will bedescribed in more detail below.

One task that the confidential data frontend 104 may be designed toperform is the gathering of confidential data from a user of the clientdevice 102. Another task that the confidential data frontend 104 may bedesigned to perform is to display insights from confidential datacontributed by other users. In order to incentivize users to providecertain types of confidential data, in an example embodiment, insightsfrom the confidential data contributed by other users are provided inresponse to the user contributing his or her own confidential data. Aswill be described in more detail, a mechanism to ensure that thecontribution of confidential data is tracked is provided.

Once the confidential data is received from the user, the confidentialdata frontend 104 may transmit the confidential data along with anidentification of the user (such as a member identification reflectingthe user's account with a social networking service) to the confidentialdata backend 106. In an example embodiment, this may be performed via,for example, a REST Application Program Interface (API).

The confidential data, along with the identification of the user, may bestored in a submission table by the confidential data backend 106 in aconfidential information database 108. In some example embodiments, thissubmission table may be encrypted in order to ensure security of theinformation in the submission table. Furthermore, in some exampleembodiments, the confidential data stored in the submission table may beencrypted using a different key than the identifying information in thesubmission table. This encryption will be described in more detailbelow.

In another example embodiment, a random transaction number is generatedfor each confidential data submission. This random transaction number isstored with the identifying information in one table, and then storedwith the confidential data in another table, with each table encryptedseparately using a different key. In either this example embodiment orthe previous example embodiment, encrypting the identifying informationseparately from the confidential data (either in one table or inseparate tables) provides added security against the possibility that amalicious user could gain access to one or the other. In other words,even if a malicious user gained access to the identifying informationby, for example, hacking the encryption used to encrypt the identifyinginformation, that would not allow the malicious user to gain access tothe confidential data corresponding to the identifying information, andvice versa. In an example embodiment, the encryption mechanism used isone that is non-deterministic, such that the same information encryptedtwice would produce different results in each encryption. In anotherexample embodiment, the transaction number itself is also encrypted,thereby preventing even the act of joining separate tables containingthe identifying information and the confidential data.

In an example embodiment, a submission table may also be able to trackwhen submissions were made by users. As such, the submission table mayinclude additional columns, such as, for example, a submissionidentification, an identification of the user who made the submission,an encryption key for the submission, and timestamp information aboutwhen the submission was made. The submission table may then be utilizedby the confidential data backend 106 to determine, for example, when toshare insights from submissions from other users to a particular user.If, for example, the user has previously submitted confidential data andhas done so recently (e.g., within the last year), then the confidentialdata backend 106 may indicate to the confidential data frontend 104 thatit should share insights from confidential data from other users withthis particular user.

There may be other methods than those described above for determiningeligibility of a user for receiving insights from submissions from otherusers. For example, a predicate expressed in terms of one or moreattributes may need to be satisfied in order to receive the insights,such as particular demographic or profile-based attributes. Theseattributes can include any such attribute, from location to title, tolevel of skill, to social networking service activities or status (e.g.,about to transition from being an active member to an inactive member),to transactional attributes (e.g., purchased a premium subscription).

Additionally, any combination of the above factors can be used todetermine whether the user is eligible for receiving insights fromsubmissions from other users.

Furthermore, the submission table may also include one or moreattributes of the user that made the submission. These attributes may beattributes that can be useful in determining a slice to which the userbelongs. Slices will be described in more detail below, but generallyinvolve a segment of users sharing common attributes, such as titles,locations, educational levels, and the like. It should be noted that itis not necessary for these attributes to be stored in the submissiontable. Since an identification of the user is available in thesubmission table, it may be possible to retrieve the attributes for theuser on an as-needed basis, such as by querying a social networkingservice with the user identification when needed.

A databus listener 110 detects when new confidential data is added tothe confidential information database 108 and triggers a workflow tohandle the new confidential data. First, the databus listener 110queries a thresholds data store 116 to determine if one or morethresholds for anonymization have been met. Specifically, until acertain number of data points for confidential data have been met, theconfidential data collection, tracking, and usage system 100 will notact upon any particular confidential data point. As will be described inmore detail later, these thresholds may be created on a per-slice basis.Each slice may define a segment of users about which insights may begathered based on data points from confidential data submitted by usersin the slice. For example, one slice may be users with the title“software engineer” located in the “San Francisco Bay Area.” If, forexample, the confidential data is compensation information, then it maybe determined that in order to gain useful insights into thecompensation information for a particular title in a particular region,at least ten data points (e.g., compensation information of tendifferent users) are needed. In this case, the threshold for “softwareengineer” located in “San Francisco Bay Area” may be set at ten. Thedatabus listener 110, therefore, is designed to retrieve theconfidential data added to the confidential information database 108,retrieve the threshold for the slice corresponding to attributes of theuser (as stored, for example, in the submission table in theconfidential information database 108 or retrieved at runtime from asocial networking service), determine if the new data point(s) cause thethreshold for the corresponding slice to be exceeded, and, if so, or ifthe threshold had already been exceeded, insert the data in a backendqueue 112 for extract, transform, and load (ETL) functions.

In an example embodiment, the thresholds data store 116 contains notjust the thresholds themselves but also a running count of how many datapoints have been received for each slice. In other words, the thresholdsdata store 116 indicates how close the slice is to having enough datapoints with which to provide insights. The databus listener 110 mayreference these counts when making its determination that a newlysubmitted data point causes a threshold to be exceeded. Running countsof data points received for each slice are updated in the thresholdsdata store 116 by the confidential data backend 106.

Since the databus listener 110 only transfers data points for aparticular slice to the backend queue 112 once the threshold for thatslice has been exceeded, the confidential data data points correspondingto that slice may need to be retrieved from the confidential informationdatabase 108 once the threshold is determined to be exceeded. Forexample, if, as above, the threshold for a particular slice is ten datapoints, the first nine data points received for that slice may simply beleft in the confidential information database 108 and not sent to thebackend queue 112. Then, when the tenth data point for the slice isstored in the confidential information database 108, the databuslistener 110 may determine that the threshold has been exceeded andretrieve all ten data points for the slice from the confidentialinformation database 108 and send them to the backend queue 112 forprocessing.

It should be noted that the information obtained by the databus listener110 from the confidential information database 108 and placed in thebackend queue 112 is anonymized. In an example embodiment, noidentification of the users who submitted the confidential data isprovided to the backend queue 112. Indeed, in some example embodiments,the information provided to the backend queue 112 may simply be theconfidential data itself and any information needed in order to properlygroup the confidential data into one or more slices. For example, ifslices are designed to group user confidential data based only on usertitle, location, and years of experience, other attributes for the userthat might have been stored in the confidential information database108, such as schools attended, may not be transferred to the backendqueue 112 when the confidential data tied to those attributes istransferred to the backend queue 112. This further helps to anonymizethe data, as it makes it more difficult for people to be able to deducethe identity of a user based on his or her attributes.

It should also be noted that any one piece of confidential data maycorrespond to multiple different slices, and thus the databus listener110 may, in some example embodiments, provide the same confidential datato the backend queue 112 multiple times. This can occur at differenttimes as well, because each of the slices may have its own thresholdthat may be transgressed at different times based on different counts.Thus, for example, compensation data for a user in the “San FranciscoBay Area” with a job title of “software developer” and a school attendedas “Stanford University” may be appropriately assigned to one slice ofsoftware developers in the San Francisco Bay Area, a slice of StanfordUniversity alums, and a slice of software developers in the UnitedStates. All slices may have their own thresholds and counts fromconfidential data from other users, who may or may not have completeoverlap with these three slices.

An ETL backend 114 acts to extract, transform, and load the confidentialdata to anonymize and group it and place it back in the confidentialinformation database 108 in a different location from where it wasstored in non-anonymized form. It should be noted that in some exampleembodiments, the anonymization described above with respect to thedatabus listener 110 may actually be performed by the ETL backend 114.For example, the databus listener 110 may send non-anonymizedconfidential data along with all attributes to the backend queue 112,and it may be the ETL backend 114 that reviews this data and discardscertain elements of it to anonymize it.

In an example embodiment, the confidential information is stored inencrypted format in the confidential information database 108 when thedatabus listener 110 sends it to the backend queue 112. As such, onefunction of the ETL backend 114 is to decrypt the confidentialinformation. Encryption and decryption of the confidential data will bediscussed in more detail below.

The ETL backend 114 writes the anonymized confidential data and sliceinformation into an ETL table corresponding to the slice in theconfidential information database 108. As described earlier, this ETLtable may be stored in a different location than that in which theconfidential data was stored initially, such as the submission tabledescribed earlier.

At a later time, and perhaps using a batch or other periodic process,the information from the ETL table may be loaded in a distributed filesystem (DFS) 118. A confidential data relevance workflow 120 may thenextract relevant information from the DFS 118 and provide one or moreinsights into the relevant information in a confidential data insightsdata store 122. A confidential data relevance API 124 may then beutilized to provide insights from the confidential data insights datastore 122 to the confidential data frontend 104, which can then displaythem to a user. As described earlier, these insights may be providedonly on a “give-to-get” basis, namely that only users who provideconfidential information (and/or have provided it recently) can viewinsights.

Turning now to more detail about the submission process, FIGS. 2A-2C arescreen captures illustrating an example of a user interface 200 providedby the confidential data frontend 104, in accordance with an exampleembodiment. Referring first to FIG. 2A, the user interface 200 here isdepicted as a screen of a standalone application operating on a mobiledevice, such as a smartphone. In FIG. 2A, the user is prompted to entera base salary in a text box 202, with a drop-down menu providing optionsfor different time periods on which to measure the base salary (e.g.,per year, per month, per hour, etc.). Additionally, the user may beidentified by name at 204, the user's title may be identified at 206,and the user's current employer may be identified at 208. Thisinformation may be pre-populated into the user interface 200, such as byretrieving this information from a member profile for the user in asocial networking service. This eliminates the need for the user toenter this information manually, which can have the effect of dissuadingsome users from providing the confidential information or completing thesubmission process, especially on a mobile device where typing orotherwise entering information may be cumbersome.

Turning to FIG. 2B, here the user interface 200 displays a number ofother possible compensation types 210-220 from which the user canselect. Selecting one of these other possible compensation types 210-220causes the user interface 200 to provide an additional screen where theuser can submit confidential data regarding the selected compensationtype 210-220. Here, for example, the user has selected “Stock” 212.Referring now to FIG. 2C, the user interface 200 then switches to thisscreen, which allows the user to provide various specific details aboutstock compensation, such as restricted stock unit (RSU) compensation 222and options 224. The user interface 200 at this stage may also displaythe other compensation types 210-220 that the user can make additionalsubmissions for.

Referring back to FIG. 2B, when the user has completed entering all theconfidential data, such as all the different compensation typesappropriate for his or her current job, a “Get insights” button 226 maybe selected, which launches a process by which the confidential databackend 106 determines whether the user is eligible to receive insightsfrom confidential data from other users and, if so, indicates to theconfidential data backend 106 that the insights should be provided.Additionally, selection of the “Get insights” button 226 represents anindication that the submission of the confidential data by this user hasbeen completed, causing the confidential data backend 106 to store theconfidential data in the confidential information database 108 asdescribed below, which then may trigger the databus listener 110 toextract the confidential information and cause the ETL backend 114 toanonymize the confidential data and place it in the appropriate ETLtables corresponding to the appropriate slices in which the confidentialdata belongs. This permits the submitted confidential data to beavailable for future insights.

FIG. 3 is a flow diagram illustrating a method 300 for confidential datacollection and storage, in accordance with an example embodiment. In anexample embodiment, the method 300 may be performed by the confidentialdata backend 106 of FIG. 1. At operation 302, confidential data isobtained. At operation 304, an identification of the user who submittedthe confidential data is obtained. It should be noted that whileoperations 302 and 304 are listed separately, they may be performed inthe same operation in some example embodiments. For example, in anexample embodiment, the confidential data frontend 104 may, uponreceiving an indication from a user that input of confidential data inthe confidential data frontend 104 by the user has been completed,forward the inputted confidential data and an identification of the userto the confidential data backend 106. In other example embodiments,however, the operations 302 and 304 may be performed separately. Forexample, in an example embodiment, the identification of the user maynot be obtained directly from the confidential data frontend 104, butrather some other type of identifying information may be obtaineddirectly from the confidential data frontend 104, and this other type ofidentifying information may be used to query a social networking serviceor other third-party service for the identification information for theuser. Regardless, after operations 302 and 304 have been performed, theconfidential data backend 106 has at its disposal some confidential dataand identification information for the user who entered the confidentialdata.

It should be noted that the confidential data may be a single piece ofinformation, or may be multiple related pieces of information. Forexample, the confidential data may simply include a total compensationvalue and nothing more, or may include a complete breakdown of differenttypes of compensation (e.g., base salary, bonus, stock, etc.).

Users are understandably concerned about the security of theconfidential information, and specifically about a malicious user beingable to correlate the confidential information and the identification ofthe user (i.e., not just learning the confidential information but tyingthe confidential information specifically to the user). As such, atoperation 306, the confidential data is encrypted using a first key andstored in a first column of a submission table in a confidentialinformation database. Then, at operation 308, the identification of theuser who submitted the confidential data is separately encrypted using asecond key and stored in a second column of the submission table in theconfidential information database.

Additionally, a number of optional pieces of information may, in someexample embodiments, be stored in the submission table at this point. Atoperation 310, a timestamp of the submission of the confidential datamay be stored in a column in the submission table. This timestamp may beused in, for example, a determination of whether the user is eligible toreceive insights from confidential data submitted by other users. Atoperation 312, one or more attributes of the user may be stored as oneor more columns in the submission table. These attributes may be used,for example, in determining to which slice(s) the confidential data mayapply, as will be described in more detail below.

FIG. 4 is a diagram illustrating an example of a submission table 400,in accordance with an example embodiment. Each row in the submissiontable 400 corresponds to a different submission. Here, the submissiontable 400 includes five columns. In a first column 402, confidentialdata encrypted by a first key is stored. In a second column 404,identification of the user who submitted the corresponding confidentialdata, encrypted by a second key, is stored. In a third column 406, atimestamp for the submission is stored. In a fourth column 408, a firstattribute of the user, here location, is stored. In a fifth column 410,a second attribute of the user, here title, is stored. Of course, theremay be additional columns to store additional attributes or other piecesof information related to the submission.

Notably, FIG. 4 depicts an example embodiment where only the first andsecond columns 402, 404 are encrypted, using different encryption keys.In some example embodiments, the additional columns 406-410 may also beencrypted, either individually or together. In some example embodiments,one or more of these additional columns 406-410 may be encrypted usingthe same key as the first or second column 402, 404. Furthermore, insome example embodiments, the submission table 400 may be additionallyencrypted as a whole, using a third encryption key different from thekeys used to encrypt the first and second columns 402, 404.

It should be noted that while FIGS. 3 and 4 describe the confidentialdata as being stored in a single column in a submission table, in someexample embodiments, this column is actually multiple columns, ormultiple sub-columns, with each corresponding to a subset of theconfidential data. For example, if the confidential data is compensationinformation, the confidential data may actually comprise multipledifferent pieces of compensation information, such as base salary,bonus, stock, tips, and the like. Each of these pieces of compensationinformation may, in some example embodiments, have its own column in thesubmission table. Nevertheless, the processes described herein withregard to the “column” in which the confidential data is stored applyequally to the embodiments where multiple columns are used (e.g., theindividual pieces of compensation information are still encryptedseparately from the user identification information).

FIG. 5 is a flow diagram illustrating a method 500 for confidential datacollection and storage, in accordance with an example embodiment. Incontrast with FIG. 3, FIG. 5 represents an example embodiment where theconfidential data and the identification of the user who submitted theconfidential data are stored in separate tables in order to provideadditional security. At operation 502, confidential data is obtained. Atoperation 504, an identification of the user who submitted theconfidential data is obtained. As in FIG. 3, while operations 502 and504 are listed separately, in some example embodiments they may beperformed in the same operation.

At operation 506, a transaction identification is generated. Thistransaction identification may be, for example, a randomly generatednumber or character sequence that uniquely identifies the submission. Atoperation 508, the transaction identification may be encrypted using afirst key. At operation 510, the transaction information (eitherencrypted or not, depending upon whether operation 508 was utilized) isstored in a first column in a first submission table and in a firstcolumn in a second submission table in a confidential informationdatabase.

At operation 512, the confidential data is encrypted using a second keyand stored in a second column of the first submission table in theconfidential information database. Then, at operation 514, theidentification of the user who submitted the confidential data isseparately encrypted using a third key and stored in a second column ofthe second submission table in the confidential information database.

Additionally, as in FIG. 3, a number of optional pieces of informationmay, in some example embodiments, be stored in the first and/or secondsubmission tables at this point. At operation 516, a timestamp of thesubmission of the confidential data may be stored in a column in thesecond submission table. This timestamp may be used in, for example, adetermination of whether the user is eligible to receive insights fromconfidential data submitted by other users. At operation 518, one ormore attributes of the user may be stored as one or more columns in thesecond submission table. These attributes may be used, for example, indetermining to which slice(s) the confidential data may apply, as willbe described in more detail below. It should be noted that whileoperations 516 and 518 are described as placing information in thesecond submission table, in other example embodiments, one or more ofthese pieces of information may be stored in the first submission table.

If operation 508 is utilized, then the fact that the transactionidentification is encrypted and is the only mechanism by which to linkthe confidential data in the first submission table with the useridentification in the second submission table through a join operationprovides an additional layer of security.

FIG. 6 is a diagram illustrating an example of a first submission table600 and a second submission table 602, in accordance with an exampleembodiment. Each row in each of the first and second submission tables600, 602 corresponds to a different submission. Here, the firstsubmission table 600 includes two columns. In a first column 604,transaction identification information encrypted by a first key isstored. In a second column 606, confidential data encrypted by a secondkey is stored.

The second submission table 602 includes five columns. In a first column608, transaction identification information encrypted by the first keyis stored. In a second column 610, identification of the user whosubmitted the corresponding confidential data, encrypted by a third key,is stored. In a third column 612, a timestamp for the submission isstored. In a fourth column 614, a first attribute of the user (herelocation) is stored. In a fifth column 616, a second attribute of theuser, here title, is stored. Of course, there may be additional columnsto store additional attributes or other pieces of information related tothe submission.

Notably, FIG. 6 depicts an example embodiment where only the first andsecond columns 608, 610 of the second submission table 602 areencrypted, using different encryption keys. In some example embodiments,the additional columns 612-616 may also be encrypted, eitherindividually or together. Furthermore, in some example embodiments, thefirst and/or second submission tables 600, 602 may be additionallyencrypted as a whole, using an additional encryption key(s) differentfrom the keys described previously.

It should be noted that while FIGS. 5 and 6 describe the confidentialdata as being stored in a single column in a first submission table, insome example embodiments this column is actually multiple columns, ormultiple sub-columns, with each corresponding to a subset of theconfidential data. For example, if the confidential data is compensationinformation, the confidential data may actually comprise multipledifferent pieces of compensation information, such as base salary,bonus, stock, tips, and the like. Each of these pieces of compensationinformation may, in some example embodiments, have its own column in thefirst submission table. Nevertheless, the processes described hereinwith regard to the “column” in which the confidential data is storedapply equally to the embodiments where multiple columns are used (e.g.,the individual pieces of compensation information are still encryptedseparately from the user identification information).

As described above, there is a need to handle situations whereconfidential data for certain combinations of cohorts, such as certaincombinations of locations and job titles, are sparse. In an exampleembodiment, a computerized matrix factorization and completion techniquemay be utilized to infer median/mean values for the confidential data.

The confidential data may be viewed in terms of a matrix where rowspertain to values of cohorts of one attribute type (such as job titles)and columns pertain to values of cohorts of another attribute type (suchas locations), with the values in each cell of the matrix comprisingsubmitted confidential data values (such as compensation values) for thecorresponding combination of cohort). Such a matrix is not full rank,meaning that there is a correlation between cohorts among the rows andcolumns, as opposed to each matrix cell being distinct and unrelated toeach other cell. For example, once confidential values are known forcertain locations, confidential values for neighboring locations may becorrelated, at least a little.

FIG. 7 is a flow diagram illustrating a method 700 of inferringmedian/mean confidential data values in accordance with an exampleembodiment. First, at operation 702, low rank approximations of thematrix may be constructed. This operation takes as input a set of medianconfidential data values for an available set of attribute cohortcombinations, along with corresponding confidence scores (if available).The confidence scores may be generated if, for example, some of themedian confidential data values have themselves been inferred via amachine learning model, which would also output a confidence scoreindicating the confidence level of the predicted median confidencevalue. Also taken as input would be a set F of candidate datatransformation functions, such as identity, natural logarithm, squareroot, and the like. In one example embodiment these candidate datatransformation functions may be monotonic. Also taken as input would bea desired error measure. This may include, for example:

-   -   1. (∥M_k−X∥_hidden)/∥X∥_hidden, where ∥X∥_hidden denotes        Frobenius norm (Euclidean norm of the matrix treated as a        vector) of matrix X restricted to the hidden entries and M_k        denotes the rank-k approximation to matrix X    -   2. The max relative deviation in the median base salary over the        hidden entries: max_{1<=i<=m, 1<=j<=n, (i,j) is hidden}        |M_k(i,j)−X(i,j)|/X(i,j), where M_k denotes the rank-k        approximation to matrix X.    -   3. The mean relative deviation in the median base salary over        the hidden entries: mean_{1<=i<=m, 1<=j<=n, (i,j) is hidden}        |M_k(i,j)−X(i,j)|/X(i,j), where M_k denotes the rank-k        approximation to matrix X.    -   4. The median relative deviation in the median base salary over        the hidden entries: median_{1<=i<=m, 1<=j<=n, (i,j) is hidden}        |M_k(i,j)−X(i,j)|/X(i,j), where M_k denotes the rank-k        approximation to matrix X.

Output of this operation may be a set of candidate low rankapproximations, corresponding to different data transformations anddifferent choices of parameters. FIG. 8 is a flow diagram illustrating amethod 702 of constructing low rank approximations of the matrix, inaccordance with an example embodiment.

For each of a plurality of different potential data transformations(e.g., each f in F), a loop is begun. At operation 802, a sparse matrixX is constructed from the set of median confidential data values afterapplying the potential data transformation f to each confidential datavalue. In general, X could contain missing entries, since thecompensation value may not be available for all (title, location) pairs.

At operation 804, a training matrix (X_train) is obtained by hiding apreset fraction of entries of the matrix X randomly (orpseudo-randomly). At operation 806, an objective function may be definedby minimizing ∥X_train−M∥² ₀+2·λ·∥M∥* such that M has rank at most k.Here, the first term refers to the Frobenius norm of the difference,restricted to non-missing entries of X_train. The second term refers tothe nuclear norm of matrix M (that is, the sum of singular values of M).

A loop is then begun for each different choice of the regularizationparameter λ and each different choice of the maximum desired rank k. Atoperation 806, M_k is computed as the matrix M that minimizes theobjective. Then, if X_train is a complete matrix with rank r, theoptimal solution is given by U. D_λ. V where:

-   -   i. U. D. V is the singular value decomposition of X_train, with        D as a diagonal matrix with entries d1, . . . , dr    -   ii. D_λ is a diagonal matrix obtained from D by performing soft        thresholding, that is, its entries are max(d1−λ, 0), . . . ,        max(dr−λ, 0).        -   b.

At operation 808, the error measure is computed by comparing therecovered matrix, M_k, and the original matrix, X, with respect to thehidden entries (these entries were not used in the above optimization,and hence can be thought of as forming the test/validation set).

At operation 810, it is determined if there are any more differentchoices of the regularization parameter λ. If so, then the method 800loops back to operation 806 for the next choice of regularizationparameter λ. If not, then at operation 812, it is determined if thereare any additional choices of maximum desired rank k. If so, then themethod 800 loops back to operation 806 for the next choice of maximumdesired rank k. If not, then at operation 814, it is determined if thereare any additional candidate data transformation functions. If so, thenthe method 800 loops back to operation 802 for the next datatransformation function.

In some example embodiments of the above method, the objective functioncould also take into account weights for different attributecombinations, for example, in terms of the confidence score:

Minimize sum_{(i,j) is present in X_train} s_conf(i,j).(X_train(i,j)−M(i,j))2+λ. ∥M∥* such that M has rank at most k, wheres_conf(i,j) is the weight for (i,j) title-region pair.

Similarly, different variants could be considered where different modelscould be constructed, such as

-   -   a. For each country.    -   b. For each function (or some other clustering of the titles        based on pay variation across regions).    -   c. A combination of the two.

Referring back to FIG. 7, at operation 704, parameters are optimized toobtain the best low rank approximation matrix. FIG. 9 is a flow diagramillustrating a method 704 for optimizing parameters to obtain the bestlow rank approximation matrix, in accordance with an example embodiment.A loop is begun for each candidate data transformation. At operation902, the matrix X_train is obtained by hiding a certain fraction ofentries of X at random (e.g., 10% so that X_train contains 90% of theentries of X). A loop is then begun for each different choice of theregularization parameter λ, and each different choice of the maximumdesired rank, k. At operation 904, M_k is computed as the matrix M thatminimizes the objective. At operation 906, the error measure isdetermined by comparing the recovered matrix, M_k and the originalmatrix, X, with respect to the hidden entries (these entries were notused in the above optimization, and hence can be thought of as formingthe test/validation set).

At operation 908, it is determined if there are any additional differentchoices of the regularization parameter λ. If so, then the method 900loops back to operation 904 for the next choice of regularizationparameter λ. If not, then at operation 910, it is determined if thereare any additional choices of maximum desired rank k. If so, then themethod 900 loops back to operation 904 for the next choice of maximumdesired rank k. If not, then at operation 912, it is determined if thereare any additional candidate data transformation functions. If so, thenthe method 900 loops back to operation 902 for the next datatransformation function.

If not, then at operation 914, the set of parameters that minimizes theabove error measure is selected, thereby obtaining the optimal datatransformation function, regularization parameter, and maximum desiredrank.

Referring back to FIG. 7, at operation 706, confidential data values forentries not present in the original matrix are inferred. FIG. 10 is aflow diagram illustrating a method 706 of inferring confidential datavalues for entries not present in the original matrix, in accordancewith an example embodiment. At operation 1002, the matrix M_opt isobtained as the matrix that minimizes the above objective under theoptimal set of parameter choices. Then a loop is begun for each (i,j)pair in M_opt, with i and j being dimensions of the matrix. At operation1004, it is determined if the entry for (i,j) is present in the originalmatrix, X. If so, then at operation 1006, that entry is output afterapplying the inverse data transformation. Otherwise, at operation 1008,M_opt(i,j) is output after applying the inverse data transformation. Atoperation 1010, it is determined if there are any more (i,j) pairs inM_opt. If so, then the method 706 loops back to operation 1004 for thenext (i,j) pair. If not, then the method 706 ends. The result is amodified matrix M_opt with inferred medians/means for sparse cells inthe original matrix.

It should be noted that it may not be beneficial to perform theseinferences for all entries in the matrix that are missing confidentialdata values (or where a median/mean could not be accurately computed orpredicted). Indeed, in certain instances, the exact combination ofattributes may not even be valid; for example, a particular job titlemay not be present in a certain location. In other instances, theinferences may simply be unreliable. However, it can be difficult todetermine when it would be appropriate to make the inferences.

In an example embodiment, a method is provided to automaticallydetermine when to perform inferences of confidential data values in amatrix. This method takes into account multiple signals to address thisproblem. First, an inference desirability score is computed forattribute combinations for which the confidential data needs to beinferred. A machine learning system for computing the inferencedesirability score for attribute combinations may be utilized, by takinginto account factors such as the member distribution, job viewdistribution, and the like.

The machine learning algorithm may be trained using a set of attributepairs along with labels denoting whether confidential data inference isdesired or not. Features for attribute combination may include, forexample, the number of members that belong to each attributecombination; the number of active members that belong to each attributecombination, where a member is considered active if he/she has loggedinto the professional social network within a recent time period; thenumber of job views corresponding to the attribute combination; thenumber of job searches corresponding to the attribute combination; thenumber of confidential data value searches corresponding to theattribute combination; the number of confidential data value insightviews corresponding to the (title, location) combination; and binarizedversions of above features, e.g., whether the number of active membersexceeds a threshold. A machine learning algorithm (such as logisticregression) is then applied to obtain a model combining differentfeatures for computing the inference desirability score.

Additionally, a machine learning system for computing the confidencescore for each inferred (title, location) combination may be utilized bytaking into account factors such as the support of entries present inthe corresponding row/column. Training data for the machine learningalgorithm can be the set of attribute pairs along with labels denotingwhether the inferred confidential data values using matrixfactorization/completion are reliable or not. Features for eachattribute combination include the number of non-missing entries for thecorresponding first attribute, the number of non-missing entries for thecorresponding second attribute, total number of confidential data valuesubmissions from users for the corresponding first attribute, totalnumber of confidential data value submissions from users for thecorresponding second attribute, combined confidence score ofconfidential data value insights for the corresponding first attribute,combined confidence score of confidential data value insights for thecorresponding second attribute, inference error for the correspondingfirst attribute (this is a measure of how close the inferred value is tothe original value, and could be computed by using the max (or mean ormedian) relative deviation in the median base salary over thenon-missing entries, or the relative error in Euclidean norm over thenon-missing entries), the inference error for the corresponding secondattribute, and binarized versions of above features, e.g., whether thetotal number of confidential data value submissions for the titleexceeds a threshold. The machine learning algorithm (such as logisticregression) can then be applied to obtain a model combining differentfeatures for computing the inference confidence score.

Additionally, a confidence interval for each attribute pair inferredconfidential data value may be inferred by:

-   -   1. repeatedly removing random number of non-missing entries from        the corresponding row and column,    -   2. applying the matrix factorization/completion based inference        algorithm, and    -   3. computing the distribution of the inferred value the        variance.

The idea is that the system can decide not to infer if the confidenceinterval is too wide.

Comparison may then be made to the expected confidential data valuerange. Specifically, gross attribute multipliers may be determined byfixing one standard attribute and computing the average confidentialdata value (possibly weighted) for each value of the first attribute,and then dividing by that for the fixed first location. For a givensecond attribute (with sufficient number of first attribute values wherethe median or mean confidential data value has been collected fromusers), divide the observed (median or mean) confidential data value foreach location by the gross multiplier, and thereby compute the empiricaldistribution of normalized confidential data values for the given secondattribute value.

Q1, Q3, IQR (Q3−Q1) may be computed, thereby computing the allowed rangeusing Box-and-Whisker method. For each location for this secondattribute value where there is an inferred confidential data value,first compute the normalized version and flag the inferred confidentialdata value if the normalized inferred confidential data value liesoutside the allowed range.

Post processing may then be performed, including the following:

-   -   1. If (inference desirability score<t1) suppress    -   2. Else if (inference confidence score<t2) suppress    -   3. Else if (the ratio of confidence interval width to the        confidential data value>t3) suppress    -   4. Else if the normalized inferred confidential data value lies        outside the allowed range suppress.

In another example embodiment, a compensation range for new attributecombinations may be inferred using matrix factorization and completiontechniques, in a similar manner as described above. In contrast to theaspects described above, the goal here is to infer the range in additionto just the median/mean. Multiple techniques based on low rank matrixapproximation and completion.

In a first technique, a joint inference of the 10^(th), 50^(th), and90^(th) percentiles may be performed. Here, an order-3 tensor, T(multi-dimensional array), is constructed wherein the dimensionscorrespond to title, location, and the median/range related values.Denoting the 10^(th), 50^(th) (median), and 90^(th) percentiles as p10,p50, p90 respectively, the three layers can be represented as:

-   -   a. (Title, location) matrix of median confidential data values    -   b. (Title, location) matrix of relative left deviation values,        that is (p50−p10)/p50    -   c. (Title, location) matrix of relative right deviation values,        that is (p90−p50)/p50

A data transformation function from a given set F of candidate datatransformation functions (such as identity, natural logarithm, squareroot, etc.) can then be applied. Tensor factorization and completion ofthe above tensor may be performed, using, for example, probabilistictensor factorization for tensor completion or simultaneous tensordecomposition and completion using factor priors, denoting the resultingtensor by T′.

For entries that were missing in the original tensor T, inferred valuesfrom the completed tensor T′ can be derived. In some exampleembodiments, a random (e.g., 10%) fraction of the entries in T to getT_train (denote the hidden entry tensor by T_test), and use T_train toperform factorization/completion and T_test to select the optimal choiceof parameters. Further layers corresponding to more percentiles may beadded if desired.

Then, an independent inference of median, left range, and right rangemay be performed. First, three (title, location) matrices can beconstructed:

-   -   a. (Title, location) matrix, X of median compensation values    -   b. (Title, location) matrix, X_left of relative left deviation        values, that is (p50−p10)/p50    -   c. (Title, location) matrix, X_right of relative right deviation        values, that is (p90−p50)/p50

Then, independent matrix factorization/completion may be performed toobtain the corresponding matrices, X′, X′_left, X′_right. For each entrynot present in the original matrix X, the inferred matrices may be usedto determine the median/relative left range/relative right range.

In another example embodiment, one matrix, which has the range (p90−p10)or the relative range (p90−p10)/p50, may be used. In this case, it maybe assumed that the inferred range is equally split on either side ofthe inferred median.

Modules, Components, and Logic

Certain embodiments are described herein as including logic or a numberof components, modules, or mechanisms. Modules may constitute eithersoftware modules (e.g., code embodied on a machine-readable medium) orhardware modules. A “hardware module” is a tangible unit capable ofperforming certain operations and may be configured or arranged in acertain physical manner. In various example embodiments, one or morecomputer systems (e.g., a standalone computer system, a client computersystem, or a server computer system) or one or more hardware modules ofa computer system (e.g., a processor or a group of processors) may beconfigured by software (e.g., an application or application portion) asa hardware module that operates to perform certain operations asdescribed herein.

In some embodiments, a hardware module may be implemented mechanically,electronically, or any suitable combination thereof. For example, ahardware module may include dedicated circuitry or logic that ispermanently configured to perform certain operations. For example, ahardware module may be a special-purpose processor, such as aField-Programmable Gate Array (FPGA) or an Application SpecificIntegrated Circuit (ASIC). A hardware module may also includeprogrammable logic or circuitry that is temporarily configured bysoftware to perform certain operations. For example, a hardware modulemay include software executed by a general-purpose processor or otherprogrammable processor. Once configured by such software, hardwaremodules become specific machines (or specific components of a machine)uniquely tailored to perform the configured functions and are no longergeneral-purpose processors. It will be appreciated that the decision toimplement a hardware module mechanically, in dedicated and permanentlyconfigured circuitry, or in temporarily configured circuitry (e.g.,configured by software) may be driven by cost and time considerations.

Accordingly, the phrase “hardware module” should be understood toencompass a tangible entity, be that an entity that is physicallyconstructed, permanently configured (e.g., hardwired), or temporarilyconfigured (e.g., programmed) to operate in a certain manner or toperform certain operations described herein. As used herein,“hardware-implemented module” refers to a hardware module. Consideringembodiments in which hardware modules are temporarily configured (e.g.,programmed), each of the hardware modules need not be configured orinstantiated at any one instance in time. For example, where a hardwaremodule comprises a general-purpose processor configured by software tobecome a special-purpose processor, the general-purpose processor may beconfigured as respectively different special-purpose processors (e.g.,comprising different hardware modules) at different times. Softwareaccordingly configures a particular processor or processors, forexample, to constitute a particular hardware module at one instance oftime and to constitute a different hardware module at a differentinstance of time.

Hardware modules can provide information to, and receive informationfrom, other hardware modules. Accordingly, the described hardwaremodules may be regarded as being communicatively coupled. Where multiplehardware modules exist contemporaneously, communications may be achievedthrough signal transmission (e.g., over appropriate circuits and buses)between or among two or more of the hardware modules. In embodiments inwhich multiple hardware modules are configured or instantiated atdifferent times, communications between such hardware modules may beachieved, for example, through the storage and retrieval of informationin memory structures to which the multiple hardware modules have access.For example, one hardware module may perform an operation and store theoutput of that operation in a memory device to which it iscommunicatively coupled. A further hardware module may then, at a latertime, access the memory device to retrieve and process the storedoutput. Hardware modules may also initiate communications with input oroutput devices, and can operate on a resource (e.g., a collection ofinformation).

The various operations of example methods described herein may beperformed, at least partially, by one or more processors that aretemporarily configured (e.g., by software) or permanently configured toperform the relevant operations. Whether temporarily or permanentlyconfigured, such processors may constitute processor-implemented modulesthat operate to perform one or more operations or functions describedherein. As used herein, “processor-implemented module” refers to ahardware module implemented using one or more processors.

Similarly, the methods described herein may be at least partiallyprocessor-implemented, with a particular processor or processors beingan example of hardware. For example, at least some of the operations ofa method may be performed by one or more processors orprocessor-implemented modules. Moreover, the one or more processors mayalso operate to support performance of the relevant operations in a“cloud computing” environment or as a “software as a service” (SaaS).For example, at least some of the operations may be performed by a groupof computers (as examples of machines including processors), with theseoperations being accessible via a network (e.g., the Internet) and viaone or more appropriate interfaces (e.g., an API).

The performance of certain of the operations may be distributed amongthe processors, not only residing within a single machine, but deployedacross a number of machines. In some example embodiments, the processorsor processor-implemented modules may be located in a single geographiclocation (e.g., within a home environment, an office environment, or aserver farm). In other example embodiments, the processors orprocessor-implemented modules may be distributed across a number ofgeographic locations.

Machine and Software Architecture

The modules, methods, applications, and so forth described inconjunction with FIGS. 1-10 are implemented in some embodiments in thecontext of a machine and an associated software architecture. Thesections below describe representative software architecture(s) andmachine (e.g., hardware) architecture(s) that are suitable for use withthe disclosed embodiments.

Software architectures are used in conjunction with hardwarearchitectures to create devices and machines tailored to particularpurposes. For example, a particular hardware architecture coupled with aparticular software architecture will create a mobile device, such as amobile phone, tablet device, or so forth. A slightly different hardwareand software architecture may yield a smart device for use in the“Internet of Things,” while yet another combination produces a servercomputer for use within a cloud computing architecture. Not allcombinations of such software and hardware architectures are presentedhere, as those of skill in the art can readily understand how toimplement the inventive subject matter in different contexts from thedisclosure contained herein.

Software Architecture

FIG. 11 is a block diagram 1100 illustrating a representative softwarearchitecture 1102, which may be used in conjunction with varioushardware architectures herein described. FIG. 11 is merely anon-limiting example of a software architecture, and it will beappreciated that many other architectures may be implemented tofacilitate the functionality described herein. The software architecture1102 may be executing on hardware such as a machine 1200 of FIG. 12 thatincludes, among other things, processors 1210, memory/storage 1230, andI/O components 1250. A representative hardware layer 1104 is illustratedand can represent, for example, the machine 1200 of FIG. 12. Therepresentative hardware layer 1104 comprises one or more processingunits 1106 having associated executable instructions 1108. Theexecutable instructions 1108 represent the executable instructions ofthe software architecture 1102, including implementation of the methods,modules, and so forth of FIGS. 1-10. The hardware layer 1104 alsoincludes memory and/or storage modules 1110, which also have theexecutable instructions 1108. The hardware layer 1104 may also compriseother hardware 1112, which represents any other hardware of the hardwarelayer 1104, such as the other hardware illustrated as part of themachine 1200.

In the example architecture of FIG. 11, the software architecture 1102may be conceptualized as a stack of layers where each layer providesparticular functionality. For example, the software architecture 1102may include layers such as an operating system 1114, libraries 1116,frameworks/middleware 1118, applications 1120, and a presentation layer1144. Operationally, the applications 1120 and/or other componentswithin the layers may invoke API calls 1124 through the software stackand receive responses, returned values, and so forth, illustrated asmessages 1126, in response to the API calls 1124. The layers illustratedare representative in nature and not all software architectures have alllayers. For example, some mobile or special-purpose operating systemsmay not provide a layer of frameworks/middleware 1118, while others mayprovide such a layer. Other software architectures may includeadditional or different layers.

The operating system 1114 may manage hardware resources and providecommon services. The operating system 1114 may include, for example, akernel 1128, services 1130, and drivers 1132. The kernel 1128 may act asan abstraction layer between the hardware and the other software layers.For example, the kernel 1128 may be responsible for memory management,processor management (e.g., scheduling), component management,networking, security settings, and so on. The services 1130 may provideother common services for the other software layers. The drivers 1132may be responsible for controlling or interfacing with the underlyinghardware. For instance, the drivers 1132 may include display drivers,camera drivers, Bluetooth® drivers, flash memory drivers, serialcommunication drivers (e.g., Universal Serial Bus (USB) drivers), Wi-Fi®drivers, audio drivers, power management drivers, and so forth dependingon the hardware configuration.

The libraries 1116 may provide a common infrastructure that may beutilized by the applications 1120 and/or other components and/or layers.The libraries 1116 typically provide functionality that allows othersoftware modules to perform tasks in an easier fashion than byinterfacing directly with the underlying operating system 1114functionality (e.g., kernel 1128, services 1130, and/or drivers 1132).The libraries 1116 may include system libraries 1134 (e.g., C standardlibrary) that may provide functions such as memory allocation functions,string manipulation functions, mathematical functions, and the like. Inaddition, the libraries 1116 may include API libraries 1136 such asmedia libraries (e.g., libraries to support presentation andmanipulation of various media formats such as MPEG4, H.264, MP3, AAC,AMR, JPG, PNG), graphics libraries (e.g., an OpenGL framework that maybe used to render 2D and 3D graphic content on a display), databaselibraries (e.g., SQLite that may provide various relational databasefunctions), web libraries (e.g., WebKit that may provide web browsingfunctionality), and the like. The libraries 1116 may also include a widevariety of other libraries 1138 to provide many other APIs to theapplications 1120 and other software components/modules.

The frameworks 1118 (also sometimes referred to as middleware) mayprovide a higher-level common infrastructure that may be utilized by theapplications 1120 and/or other software components/modules. For example,the frameworks 1118 may provide various graphic user interface (GUI)functions, high-level resource management, high-level location services,and so forth. The frameworks 1118 may provide a broad spectrum of otherAPIs that may be utilized by the applications 1120 and/or other softwarecomponents/modules, some of which may be specific to a particularoperating system or platform.

The applications 1120 include built-in applications 1140 and/orthird-party applications 1142. Examples of representative built-inapplications 1140 may include, but are not limited to, a contactsapplication, a browser application, a book reader application, alocation application, a media application, a messaging application,and/or a game application. The third-party applications 1142 may includeany of the built-in applications 1140 as well as a broad assortment ofother applications. In a specific example, the third-party application1142 (e.g., an application developed using the Android™ or iOS™ softwaredevelopment kit (SDK) by an entity other than the vendor of theparticular platform) may be mobile software running on a mobileoperating system such as iOS™, Android™, Windows® Phone, or other mobileoperating systems. In this example, the third-party application 1142 mayinvoke the API calls 1124 provided by the mobile operating system suchas the operating system 1114 to facilitate functionality describedherein.

The applications 1120 may utilize built-in operating system 1114functions (e.g., kernel 1128, services 1130, and/or drivers 1132),libraries 1116 (e.g., system libraries 1134, API libraries 1136, andother libraries 1138), and frameworks/middleware 1118 to create userinterfaces to interact with users of the system. Alternatively, oradditionally, in some systems, interactions with a user may occurthrough a presentation layer, such as the presentation layer 1144. Inthese systems, the application/module “logic” can be separated from theaspects of the application/module that interact with a user.

Some software architectures utilize virtual machines. In the example ofFIG. 11, this is illustrated by a virtual machine 1148. A virtualmachine creates a software environment where applications/modules canexecute as if they were executing on a hardware machine (such as themachine 1200 of FIG. 12, for example). A virtual machine is hosted by ahost operating system (e.g., operating system 1114 in FIG. 11) andtypically, although not always, has a virtual machine monitor 1146,which manages the operation of the virtual machine 1148 as well as theinterface with the host operating system (e.g., operating system 1114).A software architecture executes within the virtual machine 1148, suchas an operating system 1150, libraries 1152, frameworks/middleware 1154,applications 1156, and/or a presentation layer 1158. These layers ofsoftware architecture executing within the virtual machine 1148 can bethe same as corresponding layers previously described or may bedifferent.

Example Machine Architecture and Machine-Readable Medium

FIG. 12 is a block diagram illustrating components of a machine 1200,according to some example embodiments, able to read instructions from amachine-readable medium (e.g., a machine-readable storage medium) andperform any one or more of the methodologies discussed herein.Specifically, FIG. 12 shows a diagrammatic representation of the machine1200 in the example form of a computer system, within which instructions1216 (e.g., software, a program, an application, an applet, an app, orother executable code) for causing the machine 1200 to perform any oneor more of the methodologies discussed herein may be executed. Theinstructions 1216 transform the general, non-programmed machine into aparticular machine programmed to carry out the described and illustratedfunctions in the manner described. In alternative embodiments, themachine 1200 operates as a standalone device or may be coupled (e.g.,networked) to other machines. In a networked deployment, the machine1200 may operate in the capacity of a server machine or a client machinein a server-client network environment, or as a peer machine in apeer-to-peer (or distributed) network environment. The machine 1200 maycomprise, but not be limited to, a server computer, a client computer, apersonal computer (PC), a tablet computer, a laptop computer, a netbook,a set-top box (STB), a personal digital assistant (PDA), anentertainment media system, a cellular telephone, a smart phone, amobile device, a wearable device (e.g., a smart watch), a smart homedevice (e.g., a smart appliance), other smart devices, a web appliance,a network router, a network switch, a network bridge, or any machinecapable of executing the instructions 1216, sequentially or otherwise,that specify actions to be taken by the machine 1200. Further, whileonly a single machine 1200 is illustrated, the term “machine” shall alsobe taken to include a collection of machines 1200 that individually orjointly execute the instructions 1216 to perform any one or more of themethodologies discussed herein.

The machine 1200 may include processors 1210, memory/storage 1230, andI/O components 1250, which may be configured to communicate with eachother such as via a bus 1202. In an example embodiment, the processors1210 (e.g., a Central Processing Unit (CPU), a Reduced Instruction SetComputing (RISC) processor, a Complex Instruction Set Computing (CISC)processor, a Graphics Processing Unit (GPU), a Digital Signal Processor(DSP), an ASIC, a Radio-Frequency Integrated Circuit (RFIC), anotherprocessor, or any suitable combination thereof) may include, forexample, a processor 1212 and a processor 1214 that may execute theinstructions 1216. The term “processor” is intended to includemulti-core processors that may comprise two or more independentprocessors (sometimes referred to as “cores”) that may execute theinstructions 1216 contemporaneously. Although FIG. 12 shows multipleprocessors 1210, the machine 1200 may include a single processor with asingle core, a single processor with multiple cores (e.g., a multi-coreprocessor), multiple processors with a single core, multiple processorswith multiples cores, or any combination thereof.

The memory/storage 1230 may include a memory 1232, such as a mainmemory, or other memory storage, and a storage unit 1236, bothaccessible to the processors 1210 such as via the bus 1202. The storageunit 1236 and memory 1232 store the instructions 1216 embodying any oneor more of the methodologies or functions described herein. Theinstructions 1216 may also reside, completely or partially, within thememory 1232, within the storage unit 1236, within at least one of theprocessors 1210 (e.g., within the processor's cache memory), or anysuitable combination thereof, during execution thereof by the machine1200. Accordingly, the memory 1232, the storage unit 1236, and thememory of the processors 1210 are examples of machine-readable media.

As used herein, “machine-readable medium” means a device able to storeinstructions and data temporarily or permanently and may include, but isnot limited to, random-access memory (RAM), read-only memory (ROM),buffer memory, flash memory, optical media, magnetic media, cachememory, other types of storage (e.g., Erasable Programmable Read-OnlyMemory (EEPROM)), and/or any suitable combination thereof. The term“machine-readable medium” should be taken to include a single medium ormultiple media (e.g., a centralized or distributed database, orassociated caches and servers) able to store the instructions 1216. Theterm “machine-readable medium” shall also be taken to include anymedium, or combination of multiple media, that is capable of storinginstructions (e.g., instructions 1216) for execution by a machine (e.g.,machine 1200), such that the instructions, when executed by one or moreprocessors of the machine (e.g., processors 1210), cause the machine toperform any one or more of the methodologies described herein.Accordingly, a “machine-readable medium” refers to a single storageapparatus or device, as well as “cloud-based” storage systems or storagenetworks that include multiple storage apparatus or devices. The term“machine-readable medium” excludes signals per se.

The I/O components 1250 may include a wide variety of components toreceive input, provide output, produce output, transmit information,exchange information, capture measurements, and so on. The specific I/Ocomponents 1250 that are included in a particular machine will depend onthe type of machine. For example, portable machines such as mobilephones will likely include a touch input device or other such inputmechanisms, while a headless server machine will likely not include sucha touch input device. It will be appreciated that the I/O components1250 may include many other components that are not shown in FIG. 12.The I/O components 1250 are grouped according to functionality merelyfor simplifying the following discussion and the grouping is in no waylimiting. In various example embodiments, the I/O components 1250 mayinclude output components 1252 and input components 1254. The outputcomponents 1252 may include visual components (e.g., a display such as aplasma display panel (PDP), a light emitting diode (LED) display, aliquid crystal display (LCD), a projector, or a cathode ray tube (CRT)),acoustic components (e.g., speakers), haptic components (e.g., avibratory motor, resistance mechanisms), other signal generators, and soforth. The input components 1254 may include alphanumeric inputcomponents (e.g., a keyboard, a touch screen configured to receivealphanumeric input, a photo-optical keyboard, or other alphanumericinput components), point-based input components (e.g., a mouse, atouchpad, a trackball, a joystick, a motion sensor, or another pointinginstrument), tactile input components (e.g., a physical button, a touchscreen that provides location and/or force of touches or touch gestures,or other tactile input components), audio input components (e.g., amicrophone), and the like.

In further example embodiments, the I/O components 1250 may includebiometric components 1256, motion components 1258, environmentalcomponents 1260, or position components 1262, among a wide array ofother components. For example, the biometric components 1256 may includecomponents to detect expressions (e.g., hand expressions, facialexpressions, vocal expressions, body gestures, or eye tracking), measurebiosignals (e.g., blood pressure, heart rate, body temperature,perspiration, or brain waves), identify a person (e.g., voiceidentification, retinal identification, facial identification,fingerprint identification, or electroencephalogram basedidentification), and the like. The motion components 1258 may includeacceleration sensor components (e.g., accelerometer), gravitation sensorcomponents, rotation sensor components (e.g., gyroscope), and so forth.The environmental components 1260 may include, for example, illuminationsensor components (e.g., photometer), temperature sensor components(e.g., one or more thermometers that detect ambient temperature),humidity sensor components, pressure sensor components (e.g.,barometer), acoustic sensor components (e.g., one or more microphonesthat detect background noise), proximity sensor components (e.g.,infrared sensors that detect nearby objects), gas sensors (e.g., gasdetection sensors to detect concentrations of hazardous gases for safetyor to measure pollutants in the atmosphere), or other components thatmay provide indications, measurements, or signals corresponding to asurrounding physical environment. The position components 1262 mayinclude location sensor components (e.g., a Global Position System (GPS)receiver component), altitude sensor components (e.g., altimeters orbarometers that detect air pressure from which altitude may be derived),orientation sensor components (e.g., magnetometers), and the like.

Communication may be implemented using a wide variety of technologies.The I/O components 1250 may include communication components 1264operable to couple the machine 1200 to a network 1280 or devices 1270via a coupling 1282 and a coupling 1272, respectively. For example, thecommunication components 1264 may include a network interface componentor other suitable device to interface with the network 1280. In furtherexamples, the communication components 1264 may include wiredcommunication components, wireless communication components, cellularcommunication components, Near Field Communication (NFC) components,Bluetooth® components (e.g., Bluetooth® Low Energy), Wi-Fi® components,and other communication components to provide communication via othermodalities. The devices 1270 may be another machine or any of a widevariety of peripheral devices (e.g., a peripheral device coupled via aUSB).

Moreover, the communication components 1264 may detect identifiers orinclude components operable to detect identifiers. For example, thecommunication components 1264 may include Radio Frequency Identification(RFID) tag reader components, NFC smart tag detection components,optical reader components (e.g., an optical sensor to detectone-dimensional bar codes such as Universal Product Code (UPC) bar code,multi-dimensional bar codes such as Quick Response (QR) code, Azteccode, Data Matrix, Dataglyph, MaxiCode, PDF412, Ultra Code, UCC RSS-2Dbar code, and other optical codes), or acoustic detection components(e.g., microphones to identify tagged audio signals). In addition, avariety of information may be derived via the communication components1264, such as location via Internet Protocol (IP) geolocation, locationvia Wi-Fi® signal triangulation, location via detecting an NFC beaconsignal that may indicate a particular location, and so forth.

Transmission Medium

In various example embodiments, one or more portions of the network 1280may be an ad hoc network, an intranet, an extranet, a virtual privatenetwork (VPN), a local area network (LAN), a wireless LAN (WLAN), a widearea network (WAN), a wireless WAN (WWAN), a metropolitan area network(MAN), the Internet, a portion of the Internet, a portion of the PublicSwitched Telephone Network (PSTN), a plain old telephone service (POTS)network, a cellular telephone network, a wireless network, a Wi-Fi®network, another type of network, or a combination of two or more suchnetworks. For example, the network 1280 or a portion of the network 1280may include a wireless or cellular network and the coupling 1282 may bea Code Division Multiple Access (CDMA) connection, a Global System forMobile communications (GSM) connection, or another type of cellular orwireless coupling. In this example, the coupling 1282 may implement anyof a variety of types of data transfer technology, such as SingleCarrier Radio Transmission Technology (1×RTT), Evolution-Data Optimized(EVDO) technology, General Packet Radio Service (GPRS) technology,Enhanced Data rates for GSM Evolution (EDGE) technology, thirdGeneration Partnership Project (3GPP) including 3G, fourth generationwireless (4G) networks, Universal Mobile Telecommunications System(UMTS), High Speed Packet Access (HSPA), Worldwide Interoperability forMicrowave Access (WiMAX), Long Term Evolution (LTE) standard, othersdefined by various standard-setting organizations, other long rangeprotocols, or other data transfer technology.

The instructions 1216 may be transmitted or received over the network1280 using a transmission medium via a network interface device (e.g., anetwork interface component included in the communication components1264) and utilizing any one of a number of well-known transfer protocols(e.g., Hypertext Transfer Protocol (HTTP)). Similarly, the instructions1216 may be transmitted or received using a transmission medium via thecoupling 1272 (e.g., a peer-to-peer coupling) to the devices 1270. Theterm “transmission medium” shall be taken to include any intangiblemedium that is capable of storing, encoding, or carrying theinstructions 1216 for execution by the machine 1200, and includesdigital or analog communications signals or other intangible media tofacilitate communication of such software.

Language

Throughout this specification, plural instances may implementcomponents, operations, or structures described as a single instance.Although individual operations of one or more methods are illustratedand described as separate operations, one or more of the individualoperations may be performed concurrently, and nothing requires that theoperations be performed in the order illustrated. Structures andfunctionality presented as separate components in example configurationsmay be implemented as a combined structure or component. Similarly,structures and functionality presented as a single component may beimplemented as separate components. These and other variations,modifications, additions, and improvements fall within the scope of thesubject matter herein.

Although an overview of the inventive subject matter has been describedwith reference to specific example embodiments, various modificationsand changes may be made to these embodiments without departing from thebroader scope of embodiments of the present disclosure. Such embodimentsof the inventive subject matter may be referred to herein, individuallyor collectively, by the term “invention” merely for convenience andwithout intending to voluntarily limit the scope of this application toany single disclosure or inventive concept if more than one is, in fact,disclosed.

The embodiments illustrated herein are described in sufficient detail toenable those skilled in the art to practice the teachings disclosed.Other embodiments may be used and derived therefrom, such thatstructural and logical substitutions and changes may be made withoutdeparting from the scope of this disclosure. The Detailed Description,therefore, is not to be taken in a limiting sense, and the scope ofvarious embodiments is defined only by the appended claims, along withthe full range of equivalents to which such claims are entitled.

As used herein, the term “or” may be construed in either an inclusive orexclusive sense. Moreover, plural instances may be provided forresources, operations, or structures described herein as a singleinstance. Additionally, boundaries between various resources,operations, modules, engines, and data stores are somewhat arbitrary,and particular operations are illustrated in a context of specificillustrative configurations. Other allocations of functionality areenvisioned and may fall within a scope of various embodiments of thepresent disclosure. In general, structures and functionality presentedas separate resources in the example configurations may be implementedas a combined structure or resource. Similarly, structures andfunctionality presented as a single resource may be implemented asseparate resources. These and other variations, modifications,additions, and improvements fall within a scope of embodiments of thepresent disclosure as represented by the appended claims. Thespecification and drawings are, accordingly, to be regarded in anillustrative rather than a restrictive sense.

What is claimed is:
 1. A system comprising: one or more hardwareprocessors; a computer-readable medium having instructions storedthereon, which, when executed by a processor, cause the system to:obtain, using the one or more hardware processors, an anonymized set ofconfidential data values for a plurality of combinations of cohortshaving a first attribute type and a second attribute type, theconfidential data values received via a computerized user interfaceimplemented as a screen of a graphical user interface, the confidentialdata values entered into a field of the screen of the graphical userinterface; construct, using the one or more hardware processors, amatrix of the confidential data values having the first attribute typeas a first axis and the second attribute type as a second axis, witheach cell in the matrix corresponding to corresponding differentcombinations of attributes of the first attribute type and the secondattribute type; compute, using the one or more hardware processors, aset of candidate low rank approximations of the matrix using anobjective function evaluated using a set of candidate datatransformation functions, the objective function having one or moreparameters and an error function, wherein computing a set of candidatelow rank approximations includes, for each candidate data transformationfunction from the set: applying, using the one or more hardwareprocessors, the candidate data transformation function to the matrix;obtaining, using the one or more hardware processors, a training matrixby hiding a preset fraction of entries of the transformed matrix; foreach of one or more candidate parameter values for one of the one ormore parameters: computing, using the one or more hardware processors,the objective function using the candidate parameter value; andcalculating, using the one or more hardware processors, the errorfunction using the candidate parameter value; optimize, using the one ormore hardware processors, the one or more parameters that minimizes theerror function of the objective function to select one of the candidatelow rank approximations of the matrix; and infer, using the one or morehardware processors, one or more cells that are missing data, of theselected one of the candidate low rank approximations of the matrix. 2.The system of claim 1, wherein the constructing the matrix includesusing a machine learning model to generate median confidential datavalues for one or more cells along with corresponding confidence scores.3. The system of claim 1, wherein the inferring the one or more cellsthat are missing data includes: for each cell that is missing data, ofthe selected one of the candidate low rank approximations of the matrix:determining if the cell that is missing data is present in the matrix ofthe confidential data values; and in response to a determination thatthe cell that is missing data is present in the matrix of confidentialdata values, applying an inverse of the selected candidate low rankapproximations to the cell that is missing data.
 4. The system of claim1, wherein the inferring the one or more cells that are missing dataincludes: for each cell that is missing data, of the selected one of thecandidate low rank approximations of the matrix: determining if the cellthat is missing data is present in the matrix of the confidential datavalues; and in response to a determination that the cell that is missingdata is not present in the matrix of confidential data values, applyingthe selected candidate low rank approximation to a corresponding cell inan optimized matrix formed by applying the selected candidate low rankapproximation to the matrix of confidential values.
 5. The system ofclaim 1, wherein the set of candidate data transformation functionsincludes identity, log, and square root transformations.
 6. The systemof claim 1, wherein the set of candidate data transformation functionsincludes monotonic transformations.
 7. A computerized method comprising:obtaining, using a hardware processor, an anonymized set of confidentialdata values for a plurality of combinations of cohorts having a firstattribute type and a second attribute type, the confidential data valuesreceived via a computerized user interface implemented as a screen of agraphical user interface, the confidential data values entered into afield of the screen of the graphical user interface; constructing, usingthe hardware processor, a matrix of the confidential data values havingthe first attribute type as a first axis and the second attribute typeas a second axis, with each cell in the matrix corresponding tocorresponding different combinations of attributes of the firstattribute type and the second attribute type; computing, using thehardware processor, a set of candidate low rank approximations of thematrix using an objective function evaluated using a set of candidatedata transformation functions, the objective function having one or moreparameters and an error function, wherein computing a set of candidatelow rank approximations includes, for each candidate data transformationfunction: applying the candidate data transformation function to thematrix; obtaining a training matrix by hiding a preset fraction ofentries of the transformed matrix; for each of one or more candidateparameter values for one of the one or more parameters: computing theobjective function using the candidate parameter value; and calculatingthe error function using the candidate parameter value; optimizing theone or more parameters that minimizes the error function of theobjective function to select one of the candidate low rankapproximations of the matrix; and inferring one or more cells that aremissing data, of the selected one of the candidate low rankapproximations of the matrix.
 8. The method of claim 7, wherein theconstructing the matrix includes using a machine learning model togenerate median confidential data values for one or more cells alongwith corresponding confidence scores.
 9. The method of claim 7, whereinthe inferring the one or more cells that are missing data includes: foreach cell that is missing data, of the selected one of the candidate lowrank approximations of the matrix: determining if the cell that ismissing data is present in the matrix of the confidential data values;and in response to a determination that the cell that is missing data ispresent in the matrix of confidential data values, applying an inverseof the selected candidate low rank approximations to the cell that ismissing data.
 10. The method of claim 7, wherein the inferring the oneor more cells that are missing data includes: for each cell that ismissing data, of the selected one of the candidate low rankapproximations of the matrix: determining if the cell that is missingdata is present in the matrix of the confidential data values; and inresponse to a determination that the cell that is missing data is notpresent in the matrix of confidential data values, applying an theselected candidate low rank approximation to a corresponding cell in anoptimized matrix formed by applying the selected candidate low rankapproximation to the matrix of confidential values.
 11. The method ofclaim 7, wherein the set of transformation functions includes identity,log, and square root transformations.
 12. The method of claim 7, whereinthe set of candidate data transformation functions includes monotonictransformations.
 13. A non-transitory machine-readable storage mediumcomprising instructions, which when implemented by one or more machines,cause the one or more machines to perform operations comprising:obtaining, using a hardware processor, an anonymized set of confidentialdata values for a plurality of combinations of cohorts having a firstattribute type and a second attribute type, the confidential data valuesreceived via a computerized user interface implemented as a screen of agraphical user interface, the confidential data values entered into afield of the screen of the graphical user interface; constructing, usingthe hardware processor, a matrix of the confidential data values havingthe first attribute type as a first axis and the second attribute typeas a second axis, with each cell in the matrix corresponding tocorresponding different combinations of attributes of the firstattribute type and the second attribute type; computing, using thehardware processor, a set of candidate low rank approximations of thematrix using an objective function evaluated using a set of candidatedata transformation functions, the objective function having one or moreparameters and an error function, wherein computing a set of candidatelow rank approximations includes, for each candidate data transformationfunction: applying the candidate data transformation function to thematrix; obtaining a training matrix by hiding a preset fraction ofentries of the transformed matrix; for each of one or more candidateparameter values for one of the one or more parameters: computing theobjective function using the candidate parameter value; and calculatingthe error function using the candidate parameter value; optimizing theone or more parameters that minimizes the error function of theobjective function to select one of the candidate low rankapproximations of the matrix; and inferring one or more cells that aremissing data, of the selected one of the candidate low rankapproximations of the matrix.
 14. The non-transitory machine-readablestorage medium of claim 13, wherein the constructing the matrix includesusing a machine learning model to generate median confidential datavalues for one or more cells along with corresponding confidence scores.15. The non-transitory machine-readable storage medium of claim 13,wherein the inferring the one or more cells that are missing dataincludes: for each cell that is missing data, of the selected one of thecandidate low rank approximations of the matrix: determining if the cellthat is missing data is present in the matrix of the confidential datavalues; and in response to a determination that the cell that is missingdata is present in the matrix of confidential data values, applying aninverse of the selected candidate low rank approximations to the cellthat is missing data.
 16. The non-transitory machine-readable storagemedium of claim 13, wherein the inferring the one or more cells that aremissing data includes: for each cell that is missing data, of theselected one of the candidate low rank approximations of the matrix:determining if the cell that is missing data is present in the matrix ofthe confidential data values; and in response to a determination thatthe cell that is missing data is not present in the matrix ofconfidential data values, applying an the selected candidate low rankapproximation to a corresponding cell in an optimized matrix formed byapplying the selected candidate low rank approximation to the matrix ofconfidential values.
 17. The non-transitory machine-readable storagemedium of claim 13, wherein the set of candidate data transformationfunctions includes identity, log, and square root transformations.